Hello,
I have some practice math I'm working through and I'm unsure about the answer. I will also put what I got. Thanks for the help.
1. Solve using any method and identify the system as consistent, inconsistent, or dependent.
-2x+y=8
2x+2y=-8
A.) (-4,0); consistent/independent
B.) (-4,0); consistent/dependent
C.) {(-4,0 | -2x+y=8} ; consistent/dependent
D.) zero with a line through it;consistent
I thought C for this one.
2.) Solve the system using the elimination method. If the system is inconsistent or dependent, so state.
x-2y+5z=1
-x-2y+3z=-5
2x-4y+10z=3
A) (5,-3,-2)
B) (5,-4,-1)
C) dependent
D) no solution, inconsistent
I got C for this one.
3.) Solve using any method and identify the system as consistent, inconsistent, or dependent.
0.2y=0.4x+0
0.8x-0.4y=5
A.) zero with a line through it; inconsistent
B) zero with a line through it; consistent
C) zero with a line through it; dependent
D) Determination is not possible with the given information
I got A for this.
1. Should be C (IF not, then B)
2. D, if you multiply 1st equation by 2, try subtracting the third equation, and you get 0 = 5 or 0 = -1
3.
2y = 4x
8x-4y=5
-4y = 5-8x
4y = 8x-5
2y = 4x - 5/2
When minus the first equation from this, we get 0 = -5/2
So, A.
For the first question:
To solve the system of equations -2x+y=8 and 2x+2y=-8, you can choose any method you prefer - substitution, elimination, or graphing. However, in this case, it is most efficient to use elimination.
First, notice that if we multiply the first equation by 2, we get -4x+2y=16. We can see that adding this equation to the second equation will result in eliminating the variable y.
By adding the two equations together, we get (-4x+2y) + (2x+2y) = 16 + (-8), which simplifies to -2x = 8. Dividing both sides of the equation by -2 gives x = -4.
Substitute this value of x back into either of the original equations. Using the first equation, we have -2(-4) + y = 8. Simplifying further, 8 + y = 8, which gives y = 0.
Therefore, the solution to the system of equations is (-4, 0).
Now, to identify the system as consistent, inconsistent, or dependent, we can substitute these values into both equations and check if the equations are satisfied.
Substituting (-4, 0) into the first equation, we have -2(-4) + 0 = 8, which simplifies to 8 = 8. This equation is true.
Substituting (-4, 0) into the second equation, we have 2(-4) + 2(0) = -8, which simplifies to -8 = -8. This equation is also true.
Since both equations are true when the values (-4, 0) are substituted, the system is consistent.
The correct answer is A.) (-4,0); consistent/independent.
Moving on to the second question:
To solve the system of equations using the elimination method, we start by looking for a way to eliminate one of the variables. In this case, we can eliminate the x variable by adding the first equation to the second equation. This will result in canceling out the x terms.
The sum of the first and second equations is (x-2y+5z) + (-x-2y+3z) = 1 + (-5), which simplifies to -4y + 8z = -4.
Next, we can eliminate the x variable once again, but this time by adding the first equation multiplied by 2 to the third equation. This will create a new equation where the x term cancels out.
The sum of the first equation multiplied by 2 and the third equation is (2x-4y+10z) + (-x-2y+3z) = 2 + 3, which simplifies to -6y + 13z = 5.
Now, we have a system of two equations: -4y + 8z = -4 and -6y + 13z = 5. We can solve this system using either substitution or elimination method again.
However, when we try to eliminate another variable, we end up with a system that is inconsistent. The resulting equation after eliminating y in this case is 2z = 0. But this equation cannot be true since it implies that z = 0, which does not satisfy the second equation.
Therefore, the system is inconsistent, and the correct answer is D) no solution, inconsistent.
Finally, for the third question:
To solve the system 0.2y=0.4x+0 and 0.8x-0.4y=5, we can use the elimination method or substitution method.
Let's solve it using the elimination method. Since the coefficient of y in the first equation is 0.2 and the coefficient of y in the second equation is -0.4, we can multiply the first equation by 2 to make the coefficients of y the same.
Multiplying the first equation by 2 gives 0.4y = 0.8x + 0.
Now, we can add this modified first equation to the second equation: (0.4y) + (0.8x-0.4y) = 0 + 5, which simplifies to 0.8x = 5.
Dividing both sides of the equation by 0.8 gives x = 6.25.
Next, substitute this value of x back into the first equation: 0.2y = 0.4(6.25) + 0. Simplifying further, 0.2y = 2.5, which gives y = 12.5.
Therefore, the solution to the system of equations is (6.25, 12.5).
Now let's check if the system is consistent or inconsistent. By substituting (6.25, 12.5) into both equations, we can verify if they are satisfied.
Substituting (6.25, 12.5) into the first equation, we have 0.2(12.5) = 0.4(6.25) + 0. Simplifying, 2.5 = 2.5. This equation is true.
Substituting (6.25, 12.5) into the second equation, we have 0.8(6.25) - 0.4(12.5) = 5. Simplifying, 5 = 5. This equation is also true.
Since both equations are true when the values (6.25, 12.5) are substituted, the system is consistent.
However, the solution given in option A, B, C, or D does not match with the solution we obtained.
Therefore, the correct answer is D) Determination is not possible with the given information.
If you would like further clarification or have any other questions, feel free to ask!